Method and system for reference-free thermographic detection of subsurface defects using compressed image data

ABSTRACT

A method and system for non-destructive, reference-free thermographic detection of sub-surface defects uses an infrared camera to capture images of a sample that has been heated and allow to cool to equilibrium temperature. The temperature-time data obtained for each pixel in each image is converted into the logarithmic domain and a least squares fit is conducted on the data to generate a polynomial expression corresponding to the temperature-time data for a given pixel. This polynomial expression can be transformed into the original time domain to obtain temperature-time data with improved signal-to-noise characteristics. Defects can be detected by observing the zero-crossing characteristic of the second derivative of the polynomial.

REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. ProvisionalApplication No. 60/168,556, filed Dec. 2, 1999, and U.S. ProvisionalApplication No. 60/175,792, filed Jan. 12, 2000, the disclosures ofwhich are incorporated by reference herein in their entirety.

TECHNICAL FIELD

[0002] The present invention relates to the field of non-destructiveevaluation of defects in a solid sample, and more particularly to amethod and system for analyzing thermographic image data to detectsub-surface defects.

BACKGROUND OF THE INVENTION

[0003] Non-destructive evaluation of samples for sub-surface defects canbe used to check samples for weld integrity, delamination, and otherstructural defects that are not visible from observing the surface ofthe sample. Active thermography has been viewed as one option fornon-destructive testing. Generally, active thermography involves heatingor cooling the sample to create a difference between the sampletemperature and the ambient temperature and then observing the surfacetemperature of the sample as it returns to ambient temperature. Forpurposes of illustration only, the description will focus on the heatingexample, where the sample is heated via any means (e.g., flashlamps,heat lamps, forced hot air, hot air guns, electrical current, ultrasonicexcitation, etc.) and then the allowed to cool. In this type of process,the subsequent cooling is monitored using an infrared camera to detectany anomalies in the cooling behavior, which would be caused bysub-surface defects (e.g., voids, delaminations, inclusions, etc.)blocking the diffusion of heat from the sample surface to the sample'sinterior. More particularly, these defects cause the surface immediatelyabove the defect to cool at a different rate that the surroundingdefect-free areas.

[0004] As the sample cools, the infrared camera monitors and records animage sequence indicating the surface temperature, thereby creating arecord of the changes in the surface temperature over time. Thesub-surface defects can therefore be observed by viewing the output ofthe infrared camera through a display device or by capturing individualframes at selected times after the sample has been heated. This methodof visual defect identification tends to be subjective, however, and isnot suitable for automation of the defect detection process. Further, itis not possible to measure the depth of the defects simply by viewingthe infrared images.

[0005] There have been attempts to determine the depth of a defect viaprocessing and analysis of the data from the infrared camera and also toautomate the defect detection process. In some cases, the data from theinfrared camera is transferred to a computer for processing and analysisto detect variations in the cooling behavior or to perform mathematicaloperations on the data to determine the depth of the sub-surface defector other defect properties. These types of calculations, however, oftenrequire expensive low noise, high-speed digital infrared cameras.Further, the cumbersome nature of having a computer attached to thecamera for conducting calculations makes the combination impractical forapplications outside of a laboratory, such as field inspections. Also,infrared data sequences of thermal decay typically used innon-destructive testing tend to be difficult to manipulatemathematically due to low signal-to-noise ratios and large dynamic rangeand also requires a great deal of storage space.

[0006] One attempt at automating the defect detection process involvesanalyzing the contrast between each pixel in the image and a referencepixel or pixel group to generate a curve representing the amount ofcontrast between each pixel and the reference. This method requiresidentification of a reference point on the sample. The reference pointcan be a defect-free area of the sample, a separate defect-free samplethat is placed in the camera's field of view, or the mean of the entirefield of view of the camera. The temperature-time history of thisreference pixel or pixel group is subtracted from each pixel in theimage to generate a contrast vs. time plot.

[0007] Any large differences between any given pixel and the referenceindicates the presence of a defect and will exhibit itself as a peak inthe plot. The contrast vs. time plot can be measured with respect to thetime at which the peak occurs, the time at which a maximum ascendingslope occurs, and/or a moment of the curve for each pixel. Otheroptions, such as generating and displaying the contrast vs. time plotwith a reference plot and checking the point at which the two plotsseparate, is also an option.

[0008] Contrast-based methods tend to be flawed, however. In addition tothe data storage problems noted above due to the large size of theinfrared image data files, contrast-based methods require theidentification of a defect-free region on the sample as a referencepoint. This requirement is often not realistic for some samples if, forexample, the size of the defect is larger than the infrared camera'sfield of view. In such a case, there is no defect-free area availablethat can act as a reference for a given region. Further, if the entiresample exhibits a defect (e.g., a large delamination running underneaththe entire surface of the sample), there is no contrast between anyregion of the sample because the whole sample is equally or nearlyequally defective.

[0009] Contrast-based methods that rely on the mean of the entire fieldof view as a reference have also been used, but this method assumes thatthe defect area in the field is small enough so that it will notappreciably affect the mean. If a defect or group of defects occupy alarge portion of the field of view, the contrast method will beineffective because the mean value will be influenced to a large degreeby the defects, reducing any appreciable difference between the defectarea and the mean when the contrast value is calculated.

[0010] Regardless of the specific reference value used in detectingdefects, the results obtained using contrast-based methods dependsstrongly on the choice of reference region on the sample. Moreparticularly, the results obtained in contrast-based methods can beadjusted by simply changing the location of the reference region.

[0011] Further, in evaluating the results from both the contrast-basedmethods and the data obtained directly from the infrared camera,identifying the time at which a peak slope occurs (indicating thepresence of a defect) may be difficult because the signals are ofteninherently noisy, requiring the defect detection system to discriminatepixels associated with defects from noisy pixels.

[0012] There is a need for a non-destructive defect detection system andmethod that reduces the size and complexity of the temperature-timehistory of image data without sacrificing its usefulness in detectingthe location and physical characteristics of sub-surface defects.

[0013] There is also a need for a non-destructive defect detectionsystem that does not require obtaining a reference value to detectdefects by locating areas in which there is a contrast between thereference and the sample being evaluated.

[0014] There is further a need to improve the signal-to-noise ratio ofthe camera output without sacrificing spatial resolution.

SUMMARY OF THE INVENTION

[0015] Accordingly, the present invention is directed to a system andmethod for non-destructive detection of subsurface defects that avoidsthe problems encountered by currently known systems. The inventivesystem and method determines the response of a monotonically changingcharacteristic, such as temperature, of a sample over time and capturesa plurality of images as the sample characteristic changes. The imagesare used to generate a data array for each pixel in the images. The dataarray corresponds to a logarithm of the pixel amplitude and a logarithmof a given time so that a plot of monotonically changing characteristicwill be roughly linear.

[0016] A polynomial is then fitted to the data array. The polynomialcontains at least two polynomial coefficients, and typically from fiveto seven polynomial coefficients. These coefficients are analyzedinstead of the raw data in the data array, simplifying mathematicalmanipulation of the data. Because the system preferably stores andevaluates the coefficients representing the sample characteristic, andnot the sample characteristic data itself, the amount of data that needsto be stored is greatly reduced. In one embodiment, defects can bedetected by checking whether the second derivative of the polynomial hasa zero crossing. Further, the polynomial data has a highersignal-to-noise ratio than the original data, allowing the polynomialdata to serve as a less noisy substitute for the raw image data when thepolynomial data is converted from the logarithmic domain back into thelinear domain.

BRIEF DESCRIPTION OF THE DRAWINGS

[0017]FIG. 1 is a representative diagram of one embodiment of a systemimplementing the claimed invention;

[0018]FIG. 2 is a flowchart illustrating an embodiment of the inventiveprocess;

[0019]FIGS. 3a and 3 b are graphs illustrating a temperature-timecharacteristic in a linear domain and in a logarithmic domain;

[0020]FIG. 4 is a graph illustrating one example of how the inventivesystem fits a polynomial to raw data according to one embodiment of theinvention;

[0021]FIG. 5 is a flowchart illustrating one method in which theinventive system detects defects in a sample;

[0022]FIG. 6 is a graph illustrating an example of how the inventivesystem fits a polynomial to raw data according to another embodiment ofthe invention;

[0023]FIG. 7 is a representative diagram of a defect map generated bythe inventive system.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0024] As a general matter, the present invention detects subsurfacedefects using an infrared camera by observing and analyzing selectedcharacteristics of a thermal decay process. The basic foundation inwhich the inventive system operates assumes that the field of view islimited to the sample of interest. Further, the inventive system andmethod recognizes that the heated region of the sample coolsmonotonically after the heater is removed until the sample reachesequilibrium with its surroundings, that the thermal response of anypoint on the sample surface during the time interval immediately afterheating decays in such a manner that the natural logarithm of thetemperature-time response of the sample as it cools is a function thatcan be approximated by a straight line.

[0025]FIG. 1 illustrates one possible embodiment of the system used tocarry out the invention, while FIG. 2 is a flowchart illustrating oneembodiment of the inventive process. Referring first to FIG. 1, a system100 for obtaining the data to be analyzed in the inventive methodincludes at least one heat source 102, and preferably a pulsed heatsource, that heats a sample 104 to be evaluated with a pulse. The heatsource itself can be any source, such as flashlamps, heat lamps,electric current, heated air, electromagnetic induction, ultrasonicenergy, etc., but the specific choice of heat source does not matter forpurposes of the invention as long as there is a heating of the sampleand then a monotonic, exponential decrease in the sample's temperature.An infrared camera 106 obtains images of the sample, preferably in realtime, and is coupled to a computer 108 having digital image acquisitionor analog frame-grabbing capabilities to convert the data from theinfrared camera 106 to a format that can be analyzed and mathematicallymanipulated by the computer 108. Note that the computer 108 does notnecessarily need to be separate from the camera 106 and that thefunctions in the computer 108 can be incorporated into the camera itselfas, for example, an on-board chip.

[0026] Referring now to the flowchart in FIG. 2, the inventive method200 first involves heating the sample at step 202 and startingacquisition of an image sequence of the sample at step 204. The imagesequence can be stored in computer memory, videotape, or any otherelectronic storage means. Digital data corresponding to the imagesequence is then transferred to a computer or dedicated hardware formathematical analysis; note that if the data is analog data, it is firstdigitized at step 206 before it is transferred. The length of the imagesequence may depend on the type of material being inspected and thedepth at which suspected defects are located; if the material has lowthermal conductivity and/or if the suspected defects are relatively deepinside the sample, the image sequence may be lengthened. In oneembodiment, a typical image sequence from an infrared camera operatingat 60 frames per second will contain several hundred frames. In othercases, the image sequence may contain as many as several thousands offrames. The time over which the data acquisition step 206 takes placecan range over several seconds as the sample temperature returns toequilibrium, but the specific length of time will vary depending on thethermal properties of the sample. Further, the image sequence can begenerated over any time between the heating flash and the end of theimage sequence to be created, independent of the sampling rate of theinfrared camera 106.

[0027] The frames are then inspected at step 208 to locate the firstframe that is statistically stable, that is, the first frame for whichthe change in standard deviation is less than a predetermined thresholdvalue. The reason for this step is because the first several framesobtained immediately after the sample is heated may display non-linearbehavior. These frames can be detected due to large changes in thestandard deviation between consecutive frames; during normal coolingconditions, the changes in standard deviation are normally relativelysmall. Once the statistically unstable frames have been identified, theyare removed from consideration, leaving the stable frames available foranalysis.

[0028] For each individual pixel in each stable frame, the computergenerates a two-dimensional array at step 210 which is illustrated inthe example in FIG. 3b. The temperature-time characteristic of a pointon the sample will exhibit a monotonic decay, as can be seen in FIG. 3a.To simplify analysis of the temperature-time characteristic, the arraygenerated by the invention includes the natural logarithm of theamplitude of the pixel (which corresponds to the temperature at thatpoint of the sample) and the natural logarithm of the time at which thatimage was taken. The time of the first entry in the array coincides withthe first statistically stable frame, as identified at step 208. Thearray associated with each pixel and each time will exhibit generallylinear behavior, with a smaller dynamic range and a highersignal-to-noise ratio, as can be seen in FIG. 3b.

[0029] Next, a least squares fit is conducted for each two-dimensionalarray using an nth order polynomial at step 212. Note that the inventionfits a polynomial to the natural logarithm of the temperature-timecharacteristic and not to the actual temperature-time characteristic inthe linear domain. The reason is because the dynamic range of the rawtemperature-time data is too large for accurate polynomial curvefitting, and any curve that is fitted to the actual temperature-timecharacteristic tends to fit poorly and to oscillate at low signalamplitudes. The resulting function for the amplitude for a given pixelat location i,j (i=row, j=column) is defined as:

ln[I _(ij)(t)]=a ₀ +a ₁ ln(t)+a ₂ [ln(t)]² +. . . +a _(n)[ln(t)]^(n)  (1)

[0030] As can be seen from Equation 1, the resulting polynomial fromstep 212 is a continuous function obtained from the discrete data in thetwo-dimensional array, thereby allowing a user to obtain pixel amplitudevalues for time values that fall between the actual frame acquisitions.An example of the resulting temporal noise reduction and spatial noisereduction from the least squares fit is shown in FIGS. 4a and 4 b,respectively. FIG. 4a compares the raw and synthetic ln(intensity)versus ln(time) data for a sample using a sixth order polynomial, whileFIG. 4b compares the raw and synthetic intensity. As can be seen in bothfigures, the order of the polynomial is preferably relatively low andlimited to an order (e.g., seventh order) that avoids replication of thehigh-frequency noise in the infrared camera signal along with thedesired data.

[0031] Once the polynomial has been generated at step 212, each pixel isrepresented by an array of n polynomial coefficients, which willtypically be seven coefficients or less, making it unnecessary to storethe actual data sequence, which can be several hundreds or eventhousands of frames, generated by the infrared camera. Because thepolynomial representation includes only an array of coefficients, andbecause the polynomial representation of the pixel temperature-timecharacteristic is independent of the length of the data sequence, theamount of data that needs to be stored for any given pixel is greatlyreduced by the polynomial representation and much simpler to manipulatemathematically than the raw camera data. The file size for storing thepixel data is independent of the number of images taken by the camera,further reducing the memory needed to store the image data. For example,in one embodiment, the file size is the number of pixels being imagedmultiplied by the number of coefficients in the polynomial mulipled bythe number of bytes per coefficient, regardless of the

[0032] Once the polynomial representation is obtained via the naturallog transformation of the camera data, the representation can betransformed back into the original temperature-time domain by performingthe following operation: $\begin{matrix}\begin{matrix}{{I_{ij}(t)} = {\exp \left\{ {\ln\left( \left\lbrack {I_{ij}(t)} \right\rbrack \right\}} \right.}} \\{= {\exp \left\{ \left\lbrack {a_{0} + {a_{1}{\ln (t)}} + {a_{2}\left\lbrack {\ln (t)} \right\rbrack}^{2} + \ldots + {a_{n}\left\lbrack {\ln (t)} \right\rbrack}^{n}} \right\} \right.}}\end{matrix} & (2)\end{matrix}$

[0033] The function that results from this operation replicates theoriginal temperature-time data from the camera, but it will not containthe high-frequency noise that is present in the raw camera data. Thisre-transformed data can be used instead of the raw data for analysispurposes. Because the polynomial suppresses the small, high-frequencynoise variations that often occur after a certain time period haselapsed while preserving the low frequency variations caused by thermalevents, the expression that results from transforming the polynomialfunction from the logarithmic domain back to the linear domain will be asynthetic temperature-time curve that has a significantly higher signalto noise ratio than the original signal, making it more suitable forsignal analysis.

[0034] To obtain additional information about the data sequence, thefirst and second derivatives of the polynomial can be optionallycalculated at step 214. More particularly, given the expression:$\begin{matrix}{{f(t)} = {\exp \left\lbrack {\sum\limits_{i = 0}^{N}\quad {a_{1}\left\lbrack {\ln (t)} \right\rbrack}^{i}} \right\rbrack}} & (3)\end{matrix}$

[0035] the first derivative can be expressed as:

f′(t)=t ⁻¹ [Σa _(i) [ln(t)]^(i−1) ]f(t)  (4)

[0036] and the second derivative can be expressed as:

f′(t)=t ⁻¹ [Σa ₁ [ln(t)]^(i−1)]² f(t)+t ⁻² {[Σi(i−1)a _(i) [ln(t)]^(i−2) ]−[a _(i) [ln(t)]^(i−1) ]}f(t)  (5)

[0037] Images of the first and second derivatives can be generated fromEquations 4 and 5 through any means, if desired, by entering timeinformation into the polynomial, the first derivative, and/or the secondderivative. Note that because the derivatives of the image data arecalculated analytically rather than by fitting a straight line to thetangent of the noisy image data, the results obtained from thecalculated derivatives yields more accurate results than attempts tocompute the average over many noisy data points. Further, analyticalcalculation of the first and second derivatives yields results that aretrue instantaneous derivatives rather than differentials over aninterval spanning several image frames.

[0038] Because the invention focuses on differentiating and analyzingthe polynomial function instead of the raw image data, obtaininginformation about the thermal characteristics of the sample is muchsimpler because differentiating the polynomial representation is lesscomputationally complex than differentiating a noisy signal. Moreparticularly, operating on the coefficients of the polynomial, and noton the original data, eliminates the need to manipulate hundreds or eventhousands of separate images, greatly improving the speed in which theimage data can be analyzed. Also, because the first and secondderivatives are obtained by manipulating the polynomial expressionrather than conducting linear regression or curve fitting, thederivatives do not themselves contribute any noise to the final result.Further, because the invention uses noise-reduced, analyticallydifferentiated data obtained from logarithmically scaled data, the noisereduction provided by the invention allows more accurate detection ofdeeper and weaker defects as well as large defects encompassing theentire field of view.

[0039] For purposes of defect detection, only the polynomial argument(Equation 1) in the exponential expression (Equation 2) above, and notthe entire polynomial, may be used to identify sub-surface defects as analternative to using the entire exponential expression. The first andsecond derivatives of the polynomial can be applied to the time historyof each pixel (i.e. time information can be entered into the first andsecond derivatives to obtain numerical values) to generate an imagesignal with a better signal-to-noise ratio than the original polynomialexpression, thereby creating a clearer image.

[0040] Although it may be useful in some cases to calculate the completesecond derivative of Equation 2 (e.g., if the user wishes to create asynthetic sequence of second derivative images), automated defectdetection can be conducted sufficiently by differentiating Equation 1,that is, by calculating a synthetic derivative based on only thepolynomial argument rather than on the entire function.

[0041] The inventive system and method of generating polynomialequations from the image data may also be used to generate a contrastcurve by identifying a defect-free reference region of the sample orusing a separate reference sample and deriving the polynomial equationassociated with the reference, if desired. A contrast curve can then begenerated by subtracting the polynomial expression for the referencefrom the polynomial expression for each pixel; a large differencebetween the two would indicate the presence of a defect. Note thatalthough this application of the invention uses a reference region orsample, it is wholly optional.

[0042] Once steps 210 through 214 have been conducted for every pixel ata given time t, an image representation of the behavior of the sample atthat time can be scaled to match the dynamic range of the displaydevice. This scaling operation can be conducting using any commonstatistical scaling algorithm.

[0043] The image or images based on the polynomial and/or itsderivatives can be displayed on an output device, such as on a computerdisplay. The display can be a single image at a selected time t or asequence of images shown as a movie. The temporal resolution of themovie can be different than the actual data acquisition frame rate, ifdesired, to show the changes in the sample temperature more clearly;this can be conducted easily because the derived polynomial is acontinuous function, as noted above.

[0044] The particular manner in which the sample is thermally excitedand in which the data is obtained for polynomial fitting is not crucialto the invention and can be obtained in any manner. For example, thedata can be obtained from temperature-time data in an image that isscanned (e.g., systems that acquire image data as the sample is movedrelative to a heat source and an IR camera at a constant velocity,systems that move the camera and heat source relative to the sample,etc.).

[0045]FIG. 5 is a flowchart illustrating how the generated polynomial isused in defect detection. Before the actual measurement takes place, thesystem can be calibrated to determine defect depth and area at step 500.If a depth of a particular defect in the sample is known, this defectcan be used to calibrate the defect map according to the relationship:

Depth=A(t _(zerocross))^(1/2)  (6)

[0046] By using a known depth and known corresponding zero crossingtime, the constant A can be determined from the above equation.

[0047] Spatial calibration can also be conducted by placing an objecthaving known dimensions in the camera's field of view and then countingthe number of pixels required to create the image of the object. Thisinformation generates a value corresponding to the area covered by asingle pixel at a fixed distance from the camera.

[0048] As explained above and shown in FIG. 2, the system firstgenerates a polynomial expression and a first and a second derivativefor each pixel at each point in time at steps 212 and 214. Next, foreach pixel, the computer 108 determines the logarithm of the time atwhich the earliest zero crossing for each pixel occurs at steps 502 and504. If no such time exists, then the pixel is considered defect-freeand the pixel is assigned a reserved value corresponding to a particularcolor or color group at step 503. The process then repeats for all ofthe pixels in the image at step 506. Once the second derivative for allof the pixels have been obtained for the entire data sequence, the zerocrossing times and/or the reserved values are placed in a twodimensional array, creating a defect map of the data sequence.

[0049] Once the defect map has been created, the logarithm of the zerocrossing time is converted back to the time domain at step 508 by takingits exponential as follows:

t _(zerocross)=exp(ln(t _(zerocross)))  (7)

[0050] The exponential of the defect map array can then be displayed asan image by, for example, mapping the array to a mapped color palettewhere selected colors are assigned to numerical values. Pixels that donot have any zero crossings may be mapped to a selected color ordisplayed at a gray scale value that is proportional to the pixelamplitude at a particular time after flash heating. Preferably, theresultant defect map array will show the defects in colors thatcorrespond to the depth of the defect and that are superimposed on auniform selected color or gray scale image of the sample showing thenormal sub-surface structure of the sample. A representative example ofsuch a defect map is shown in FIG. 7.

[0051] If the system has been calibrated according to step 500 above,the invention can then determine the defect depth and area at step 510.To determine the defect depth, the system uses the constant Acorresponding to the material composition of the sample. Constant A iscalculated from the temperature-time information of a defect havingknown dimensions (i.e., A can be readily calculated from Equation 6 ifthe zero-crossing time and the depth are known for a reference defect).To determine the defect area, the total number of pixels havingzero-crossing values are counted and multiplied by the single pixelarea. The defect area value can be significant because the criteria forrejecting a sample is often based on the defect area.

[0052] As can be seen above, no reference value is required to detectsub-surface defects. As a result, the invention can detect defects evenin a sample that has a defect spanning the entire sample.

[0053] The above process can be used to pre-process any images from aninfrared camera for further analysis, such as peak slope or peakcontrast time measurements, breakpoint analysis, pulse phase lock-in,etc. The pre-processing steps described above generate an image signalwith much of its temporal noise removed, yielding more accurate resultsin any additional processes.

[0054] Although the above examples focus on using a single polynomialexpression to describe the temperature-time characteristic for a givensample, more than one polynomial expression may be desired to addressthe thermal behavior at the extremes of the temperature timecharacteristic and prevent the extremes from skewing the analysis of thetemperature-time behavior of the sample. More particularly, withreference to FIG. 6, the polynomial fit when using one polynomial may beadversely affected by the temperature-time curve behavior at the veryearly and very late stages. As noted above, in the early stagesimmediately after flash heating, the infrared camera data may becomebriefly saturated and may initially display non-linear behavior thatdoes not reflect the thermal characteristics of the sample accurately.In the late stages, the temperature-time characteristic of the sampletends to be weaker and therefore more susceptible to noise and/ortemperature fluctuations due to convection or stray radiation.

[0055] To prevent the extreme portions of the temperature-timecharacteristic from affecting the results in the central region, theexample shown in FIG. 6 uses more than one polynomial equation todescribe the complete temperature-time history of each pixel. In theexample shown in the Figure, the temperature-time characteristic isdivided into early, intermediate, and late behavior regions, 600, 602and 604 respectively, each of which exhibit slightly different temporalbehavior, and each region is described using a different low-orderpolynomial. When viewed separately, the temperature-time characteristicfor each individual region 600, 602, 604 behaves more like a linearfunction than a single plot of the entire time sequence. As a result,each separate region is more easily approximated by a low-orderpolynomial than the entire temperature-time plot.

[0056] Detecting defects using the polynomial for each region is thesame as described above. More particularly, the processor can calculatefirst and second derivatives of one or more of the polynomials. Further,as explained above, the zero crossing behavior of the second derivativecan be used to determine the depth of a defect. Note that the defectdepth can also be determined by finding the point in time at which thefirst derivative of the polynomial deviates from −0.5 by a predeterminedthreshold. The −0.5 value is generated based on the known temperaturecharacteristic of a semi-infinite solid that has been instantaneouslyflash-heated, which can be described as: $\begin{matrix}{T = \frac{Q}{{e(t)}^{\frac{1}{2}}}} & (8)\end{matrix}$

[0057] where e is the thermal effusivity of the material (the squareroot of the product of the density, thermal conductivity and heatcapacity), Q is the energy input to the sample by the flash-heating, andt is the elapsed time after flash-heating. When the natural logarithm ofthe equation is taken, the resulting expression is:

ln(T)=(Q/a)−0.5 ln(t)  (9)

[0058] As can be seen in the above equation, the natural logarithm ofthe temperature-time data includes a time-dependent term with a slope of−0.5 that is independent of material properties.

[0059] During sample evaluation, the above two equations are usefulbecause a sample will behave like a semi-infinite sample, such that thenatural logarithm of the temperature-time data has a slope of −0.5, asheat propagates from the surface into the bulk of the sample until adefect is encountered. If there is a defect in the sample, thetemperature-time data will deviate from the −0.5 slope. As a result, thefirst derivative expression can be used to detect defects by checkingwhether the first derivative for a given pixel deviates from −0.5 basedon this equation.

[0060] As a result, the inventive system and method generates a datastructure, which is based on the original data sequence obtained fromthe infrared camera, that is more compact, easier to manipulatemathematically, and less prone to temporal noise than the original datasequence but that still preserves the characteristics that indicate thepresence of sub-surface defects. By reducing temporal noise, theinventive system allows relatively inexpensive infrared cameras to beused in the system. Further, because the data generated by the inventionis much smaller than the image data obtained from the camera, the storeddata can be differentiated and integrated with respect to time moreeasily than the original data generated by the camera. The analysis andmanipulation of the data from the camera can be conducted in anautomated fashion, without any user intervention or adjustment.

[0061] The inventive system can be used alone or as a pre-processingstep in conjunction with other methods for measuring, characterizing,and/or recognizing defects or sample material properties. Although theabove-described configuration uses an infrared camera to acquire thedata and transfers the data to a computer for further processing, theentire system can be incorporated into the camera itself without aseparate computer. Also, although the above example analyzes infraredimage data, the inventive system and method can be applied to any dataset that is in response to a stimulus that causes a monotonicallyincreasing or decreasing response and where there is no random motion inthe field of view in which the data is generated.

[0062] It should be understood that various alternatives to theembodiments of the invention described herein may be employed inpracticing the invention. It is intended that the following claimsdefine the scope of the invention and that the method and apparatuswithin the scope of these claims and their equivalents be coveredthereby.

What is claimed is:
 1. A system for determining a time response to amonotonically changing characteristic of a sample, comprising: a camerathat obtains a plurality of images of the sample over time, each imagehaving a plurality of pixels, each pixel having an amplitudecorresponding to the monotonically changing characteristic of thesample; and a processor that receives the plurality of images andgenerates a data array for at least a portion of the plurality ofpixels, the data array corresponding to a logarithm of the pixelamplitude at a given time and a logarithm of the given time, wherein theprocessor fits a polynomial to at least a portion of the data array, thepolynomial having at least one polynomial coefficient, such that eachpixel in said portion of plurality of pixels is represented by acoefficient array containing said at least one polynomial coefficient.2. The system of claim 1, wherein the camera is an infrared camera. 3.The system of claim 1, wherein the processor is in a computer.
 4. Thesystem of claim 1, wherein the processor is located on the camera. 5.The system of claim 1, wherein the processor calculates an instantaneousfirst derivative of the polynomial for a specified time value.
 6. Thesystem of claim 5, wherein the processor determines whether the firstderivative for each pixel over time deviates from −0.5 by apredetermined threshold.
 7. The system of claim 5, wherein the processorcalculates an instantaneous second derivative of the polynomial for aspecified time value.
 8. The system of claim 7, wherein the processordetermines whether the second derivative for each pixel has a zerocrossing, wherein the presence of the zero crossing indicates adefective pixel and the absence of the zero crossing indicates adefect-free pixel.
 9. The system of claim 8, wherein the processorconverts the logarithm of the earliest zero crossing time into a lineartime domain for defective pixels, assigning a reserved value fordefect-free pixels, and using the reserved value and the converted zerocrossing time for each pixel to generate a defect map array that uses afirst color value for defective pixels and a second color value fordefect-free pixels.
 10. The system of claim 1, wherein the processorgenerates a reference polynomial and subtracts the polynomial associatedwith each pixel in said portion of plurality of pixels from thereference polynomial to generate a contrast curve, wherein a peak in thecontrast curve indicates the presence of a subsurface defect.
 11. Thesystem of claim 1, wherein the processor fits a first polynomial to afirst portion of the data array and a second polynomial to a secondportion of the data array.
 12. The system of claim 1, wherein theprocessor divides the data array into an early region, an intermediateregion, and a late region and fits a first polynomial to the earlyregion, a second polynomial to the intermediate region, and a thirdpolynomial to the late region.
 13. The system of claim 1, furthercomprising a memory that stores said coefficient array.
 14. The systemof claim 13, wherein the coefficient array is stored in the memory as afile having a size that is independent of the number of images obtainedby the camera.
 15. A system for determining a time response to atemperature change in a sample, comprising: means for changing thetemperature of the sample; a camera that obtains a plurality of imagesof the sample over time, each image having a plurality of pixels eachhaving an amplitude corresponding to the temperature of the sample; anda processor that receives the plurality of images and generates a dataarray for each of said plurality of pixels, the data array correspondingto a logarithm of the pixel amplitude at a given time and a logarithm ofthe given time, wherein the processor fits a polynomial to at least aportion of the data array, the polynomial being in the logarithmicdomain and having at least two polynomial coefficients, such that eachpixel in said plurality of pixels is represented by a coefficient arraycontaining said at least two polynomial coefficients, and wherein theprocessor calculates at least one of an instantaneous first derivativeand an instantaneous second derivative of each polynomial for a giventime value.
 16. The system of 15, wherein the processor determineswhether the first derivative for each pixel over time deviates from −0.5by a predetermined threshold.
 17. The system of claim 15, wherein theprocessor determines whether the second derivative for each pixel has azero crossing, wherein the presence of the zero crossing indicates adefective pixel and the absence of the zero crossing indicates adefect-free pixel.
 18. The system of claim 17, wherein the processorconverts the logarithm of the earliest zero crossing time into a lineartime domain for defective pixels, assigning a reserved value fordefect-free pixels, and using the reserved value and the converted zerocrossing time for each pixel to generate a defect map array that uses afirst color value for defective pixels and a second color value fordefect-free pixels.
 19. The system of claim 18, wherein the first colorvalue is selected from a mapped color palette and the second color valueis selected from a gray scale such that the defect map shows the defectin a color that corresponds to a depth of the defect and that issuperimposed on the gray scale image of the sample.
 20. The system ofclaim 15, wherein the processor generates a reference polynomial andsubtracts the polynomial associated with each pixel in said portion ofplurality of pixels from the reference polynomial to generate a contrastcurve, wherein a peak in the contrast.
 21. The system of claim 15,wherein the processor fits a first polynomial to a first portion of thedata array and a second polynomial to a second portion of the dataarray.
 22. The system of claim 15, wherein the processor divides thedata array into an early region, an intermediate region, and a lateregion and fits a first polynomial to the early region, a secondpolynomial to the intermediate region, and a third polynomial to thelate region.
 23. The system of claim 15, further comprising a memorythat stores said coefficient array.
 24. The system of claim 23, whereinthe coefficient array is stored in the memory as a file having a sizethat is independent of the number of images obtained by the camera. 25.The system of claim 15, wherein the processor determines a defect area.26. A method for determining a time response to a monotonic change in acharacteristic of a sample, comprising the steps of: obtaining aplurality of images of the sample over time, each image having aplurality of pixels each having an amplitude corresponding to themonotonically changing characteristic of the sample; generating a dataarray for each of the plurality of pixels, the data array correspondingto the logarithm of the pixel amplitude at a given time and thelogarithm of the given time; and fitting a polynomial to the data arrayassociated with at least a portion of the plurality of pixels, thepolynomial having at least two polynomial coefficients, such that eachpixel in said portion of plurality of pixels is represented by acoefficient array containing said at least two polynomial coefficients.27. The method of claim 26, further comprising the step of calculatingan instantaneous first derivative of the polynomial for a specified timevalue.
 28. The method of claim 27, further comprising the step ofdetermining whether the first derivative for each pixel over timedeviates from a slope of −0.5.
 29. The method of claim 27, furthercomprising the step of calculating an instantaneous second derivative ofthe polynomial for a specified time value.
 30. The method of claim 29,further comprising the step of determining whether the second derivativefor each pixel has a zero crossing, wherein the presence of the zerocrossing indicates a defective pixel and the absence of the zerocrossing indicates a defect-free pixel.
 31. The method of claim 30,further comprising the step of converting the logarithm of the zerocrossing time into a linear time domain for defective pixels, assigninga reserved value for defect-free pixels, and using the reserved valueand the converted zero crossing time for each pixel to generate a defectmap array that uses a first color value for defective pixels and asecond color value for defect-free pixels.
 32. The method of claim 26,further comprising the step of generating a reference polynomial andsubtracts the polynomial associated with each pixel in said portion ofplurality of pixels from the reference polynomial to generate a contrastcurve, wherein a peak in the contrast curve indicates the presence of asubsurface defect.
 33. The method of claim 26, further comprising thestep of fitting a first polynomial to a first portion of the data arrayand a second polynomial to a second portion of the data array.
 34. Themethod of claim 26, further comprising the step of dividing the dataarray into an early region, an intermediate region, and a late regionand fits a first polynomial to the early region, a second polynomial tothe intermediate region, and a third polynomial to the late region. 35.The method of claim 26, further comprising the step of storing thecoefficient array in a memory.
 36. The method of claim 35, wherein thecoefficient array is stored in the memory in a file having a size thatis independent of the number of images obtained by the camera.